Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body Problem

In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well.Comment: 9 pages, 14 figure

SUSY transformation of the Green function and a trace formula

An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous spectrum is present the trace of the difference of the Green functions for SUSY partners is a finite quantity which may or may not be equal to zero despite the divergence of the traces of each Green function. Our findings are illustrated by using the free particle example considered both on the whole real line and on a half line

Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficients related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of $\sim 0.035$ (for the above mentioned filter), below which individuals are at risk.Comment: 5 latex pages (including 6 figures). Accepted in Fractal

A new HW Vir binary from the Palomar Transient Factory: PTF1 J072455.75+125300.3 - An eclipsing subdwarf B binary with a M-star companion

We report the discovery of an eclipsing binary -- PTF1 J072456$+$125301-- composed of a subdwarf B (sdB) star ($g'=17.2^m$) with a faint companion. Subdwarf B stars are core helium-burning stars, which can be found on the extreme horizontal branch. About half of them reside in close binary systems, but few are known to be eclipsing, for which fundamental stellar parameters can be derived.\newline We conducted an analysis of photometric data and spectra from the Palomar 60'' and the 200" Hale telescope respectively. A quantitative spectral analysis found an effective temperature of $T_{\text{eff}}=33900\pm350$\,K, log g = $5.74\pm0.08$ and log($n_{\text{He}}/n_{\text{H}}) = -2.02 \pm0.07$, typical for an sdB star. The companion does not contribute to the optical light of the system, except through a distinct reflection effect. From the light curve an orbital period of 0.09980(25)\,d and a system inclination of 83.56\pm0.30\,^{\circ} were derived. The radial velocity curve yielded an orbital semi-amplitude of K_1=95.8\pm 8.1\,\text{km s^{-1}}. The mass for the M-type dwarf companion is $0.155\pm0.020\,M_{\odot}$. PTF1\,J072456$+$125301 has similar atmospheric parameters to those of pulsating sdB stars (V346 Hya stars). Therefore it could be a high-priority object for asteroseismology, if pulsations were detected such as in the enigmatic case of NY Vir.Comment: Accepted to A&A, 7pages, 4 figure

Changes at Work

Assesses the changing nature of work, the meaning of work, dissatisfaction with work, and interest in work reform.https://research.upjohn.org/up_press/1137/thumbnail.jp